(1) Field of the Invention
The present invention relates to a technique for assessing the performance of a transmission electron microscope or a method for measuring an information transfer limit that is a major factor for determining a spatial resolution offered by an electron microscope, and a transmission electron microscope to which the measuring method is adapted.
(2) Description of the Related Art
In transmission electron microscopes, a resolution is the most important index of performance. The resolution falls into multiple different definitions such as a point resolution, a lattice resolution, and an information transfer limit that are conventionally used for different purposes.
Among the definitions, the point resolution refers to a resolution that provides a limit to which the structure of an observational entity such as an atomic structure in a specimen can be visualized correctly. When it says that the structure can be visualized correctly, it means that the changes in the phase and amplitude of an electron beam occurring when the electron beam passes through a specimen can be correctly reproduced on an image formation plane. If we observe an entity smaller than the point resolution, the phase of an electron beam cannot be correctly reproduced due mainly to spherical aberration caused by an objective lens. Consequently, the point resolution is the direct index of performance from the viewpoint of observing the structure of an observational entity.
In contrast, the information transfer limit refers to a limit of a resolution determined when the contrast of an electron beam (that is, a difference in the intensity=|amplitude|2 of an electron beam) is damped due to the incoherency of the electron beam caused by energy dispersion or angular dispersion.
In normal electron microscopes, the point resolution is larger than the information transfer limit. Therefore, when a specimen is observed using an electron beam that provides a spatial frequency equal to or larger than the information transfer limit, any contrast is manifested in a micrograph according to a degree of scattering (that is, information on a specimen) caused by the specimen. However, when a specimen is observed using an electron beam that provides a spatial frequency equal to or smaller than the point resolution, since the phase of the electron beam is not correctly reproduced, an image formed does not always correctly reflect the structure of an observational entity. For example, a structure that should appear in black may appear in white.
What explicitly indicates the relationship between an observational entity and an image is a phase contrast transfer function described in, for example, “Principles and Usage of High-resolution Electron Microscope” by Shigeo Horiuchi (1988, Kyoritsu Shuppan Co., Ltd., ISBN 4-320-07123-9, P. 146). FIG. 1A shows an example. Parameters employed are an accelerating voltage that is set to 200 kV, a degree of electron beam energy dispersion that is set to 2×10−6, a spherical aberration coefficient Cs that is set to 1.5 mm, a chromatic aberration coefficient Cc that is set to 2.5 mm, a focal spread Δ in the direction of the optical axis of an electron microscope caused by the chromatic aberration which is set to 8.3 nm, a degree of angular dispersion γ of an electron beam that is set to 1.0×10−5 rad, and a defocus length df that is set to +73.5 nm.
The axis of abscissas of the graph indicates a spatial frequency u equivalent to the size of an observational object, and the axis of ordinates indicates an amplitude with the amplitude of an incident electron beam regarded as 1. A curve 1a represents a phase contrast transfer function that reflects even an adverse effect of spherical aberration, and vibrates to signify that when the spatial frequency u is higher than about 4.0 nm−1, reproduction of a phase becomes incomplete. Namely, in this example, the spatial frequency u associated with a point resolution is 4.0 nm−1, and the point resolution ds is 0.25 nm.
On the other hand, as for contrast damping phenomena derived from energy dispersion of an electron beam and angular dispersion thereof respectively, as seen from a damping curve 2a and a damping curve 3a, the former contrast damping derived from energy dispersion is dominant. Namely, even when the imperfection in a phase expressed by the curve 1a is ignored, as the structure of an observational entity gets smaller, a contrast damps. On the contrast damping curve 2a expressing the contrast damping derived from energy dispersion and the contrast damping curve 3a expressing the contrast damping derived from angular dispersion, a point at which the amplitude assumes a certain defined value (for example, 1/e where e denotes the base of a natural logarithm) shall be defined to indicate the information transfer limit. In the example of the graph, the spatial frequency u associated with the information transfer limit is 4.1 nm−1, and a resolution of the information transfer limit dc is 0.24 nm. As mentioned above, in a conventional electron microscope, ds>dc is established. A substantial resolution offered by the electron microscope is represented by the point resolution.
In the late 1990's, a spherical aberration corrector employing a multipole electron lens was put to practical use. When a phase shift caused by spherical aberration can be corrected, the relationship between the values of a point resolution and an information transfer limit may sometimes be reversed to be ds<dc. In this case, the information transfer limit substantially determines a resolution to be offered by an electron microscope. FIG. 1B introduces an example of a phase contrast transfer function defined under the condition. A curve 1b represents a phase contrast transfer function that reflects even an adverse effect of a spherical aberration. Compared with FIG. 1A, the spherical aberration coefficient Cs is corrected to be 15×10−3 mm, and the defocus length df is set to +15.0 nm. Since the spherical aberration coefficient Cs is corrected, even when the spatial frequency u is so high as to exceed 5 nm−1, a phase can be correctly reproduced. Moreover, unlike the curve 1a shown in FIG. 1A, the curve 1b does not vibrate relative to even high spatial frequencies. The spatial frequency u associated with a point resolution is 5.6 nm−1, and the point resolution ds is equal to 0.18 nm.
On the other hand, since the spherical aberration alone is corrected, a damping curve 2b expressing contrast damping derived from energy dispersion does not change from the curve 2a shown in FIG. 1A. Consequently, an information transfer limit is the same as the one in the case in FIG. 1A where the spherical aberration is not corrected. The spatial frequency u associated with the information transfer limit is 4.1 nm−1, and the information transfer limit dc is 0.24 nm. Consequently, ds<dc is established. In this case, a resolution offered by an electron microscope is substantially restricted by the information transfer limit. Hereinafter, if the practical use of a transmission electron microscope with an aberration corrector further prevails, the information transfer limit will be presumably noted as an index of performance determining a resolution.
Methods for measuring an information transfer limit of a transmission electron microscope includes a method of observing an amorphous thin film, which is made of carbon, germanium, or tungsten, by setting an electron microscope at a high magnification, and producing a diffractgram (that is, a light-diffracted image of a micrograph or a Fourier-transformed image thereof). Since the amorphous thin film has a random structure, it is thought to include structures exhibiting various spatial frequencies (that is, having various sizes). Namely, When the amorphous thin film is observed using the electron microscope, a spatial frequency serving as a limit of the spatial frequencies exhibited by structures correctly reflected on a formed electron micrograph is inspected.
FIG. 2A shows an example of measurement based on a diffractgram produced by a field-emission transmission electron microscope to which an accelerating voltage of 1 MV is applied. In the diffractgram, a pattern of numerous rings appears. The ring pattern is associated with the fluctuation in an amplitude plotted as the vibration of the curve 1a representing the phase contrast transfer function in FIG. 1A. Namely, it can be said that an effective signal can be sensed while being discriminated from a background such as noise within a range of frequencies within which the rings are seen. Consequently, an information transfer limit can be estimated as a frequency limit to which the rings are discerned. In the example shown in FIG. 2A, the information transfer limit is about 0.1 nm.
The merit of the method lies in that an information transfer limit can be grasped two-dimensionally. Not only the information transfer limit but also an adverse effect such as aberrations caused by a lens, mechanical vibrations, or electromagnetic noise can be discerned. For example, when a lens causes astigmatism, a circular ring pattern in a diffractgram is shown to warp in the azimuth of the astigmatism. Moreover, if the mechanical vibrations occur, the pattern decays anisotropically to reflect the directivity of the vibrations.
As an extension of the method, there is a method of observing the same position in an amorphous thin film multiple times, checking a cross-correlation between images or the dependency on a spatial frequency, and estimating an information transfer limit. Specifically, a micrograph of the same position in an amorphous thin film is double exposed on the same film with the film slightly shifted, and a diffractgram (Fourier-transformed pattern) of images resulting from the double exposure is produced. If the double-exposure images have a correlation, Young fringes being spaced by a distance corresponding to a magnitude of parallel shift, by which the film is shifted for exposures, would appear in the diffractgram.
FIG. 2B shows an example of measurement (cited from “Breaking the spherical and chromatic aberration barrier in transmission electron miscroscopy” by B. Freitag, S. Kujawa, P. M. Mul, J. Ringnaldar, and P. C. Tiemeijer (Ultramicroscopy, Vol. 102, 2005, p. 209214). A pattern of parallel stripes running from right obliquely up to left obliquely down is called Young fringes. Double-exposure images have a correlation within a range of spatial frequencies within which the Young fringes are discerned. In other words, an effective signal is considered to be sensed within the range of spatial frequencies. Consequently, an information transfer limit can be estimated. In the example shown in FIG. 2B, the information transfer limit is estimated as a limit of the range of spatial frequencies within which the fringes are discerned, that is, approximately 0.07 nm.
The measuring method does not depend on a pattern (the rings in FIG. 2A) that derives from aberrations caused by an objective lens, but can assess a specimen on the basis of the correlation between two micrographs. The measuring method is therefore suitable for assessment of an information transfer limit of a transmission electron microscope that includes a spherical aberration corrector and has the spherical aberration, which is caused by an objective lens, corrected. In reality, FIG. 2B shows the pattern formed by an electron microscope which has aberrations corrected and to which an accelerating voltage of 300 kV is applied. A ring pattern stemming from spherical aberration caused by an objective lens and being seen in FIG. 2A does not appear because the aberration has been corrected. In other words, the method adopted in the case shown in FIG. 2A cannot measure an information transfer limit of the aberration-corrected electron microscope.
The two techniques are such that an amorphous thin film is observed using an electron microscope in order to determine an information transfer limit of the electron microscope. Chromatic aberration and spherical aberration caused by an objective lens are major factors that determine an information transfer limit according to the energy dispersion and angular dispersion of an electron beam. FIG. 3 schematically shows the relationship among a specimen, the objective lens, and an enlarged image. An electron beam 4 perpendicularly incident on a specimen surface of an amorphous thin film 5 along the optical axis 30 of an electron microscope becomes a transmitted wave g0, which has been transmitted by the amorphous thin film 5 that is a specimen to be observed, or scatters to become diffracted waves gk (where k denotes ±1, ±2, ±3, etc.). An image is formed on an (enlarged) image plane 8 by an objective lens 7.
In FIG. 1A and FIG. 1B, the damping curves 2a and 2b that represent contrast damping derived from energy dispersion of an electron beam and that are used to determine an information transfer limit are plotted to express a fading rate of the amplitude of an electron beam on the image formation plane 8 in relation to the spatial frequency U with the amplitude on the specimen surface of the amorphous thin film 5 as a reference. Once the amplitudes of the electron beam attained on the specimen surface of the amorphous thin film 5 and the image formation plane 8 respectively are known, a damping curve can be plotted and an information transfer limit can be determined. The amplitude on the image plane 8 can be measured because the electron beam can be observed as an enlarged image on the image plane. However, the value of the amplitude of the electron beam coming out of the specimen surface of the amorphous thin film 5 before passing through the objective lens is generally unknown.
As preconditions for use of the amorphous thin film 5, the structure of the amorphous thin film should be regarded as a random structure, and the distribution of spatial frequencies u should be regarded as being nearly continuous and uniform over a range of frequencies concerned (for example, from 1 nm−1 to 0.1 nm−1). The diffraction angle 2β of an electron beam on a specimen and the spatial frequency u have a relationship of 2β=λu where λ denotes the wavelength of the electron beam.
Consequently, as illustratively shown in FIG. 3, the diffracted waves gk (where k denotes ±1, ±2, ±3, etc.) work like conical homogeneous continuous light, which has the light source thereof placed on a specimen surface, over an angular range that defines an area where the spatial frequencies u are regarded as being uniform, and that ends with the objective lens 7. As long as the amplitude on the side of a specimen is regarded as being constant, the diffractgram shown in FIG. 2A expresses a phase contrast transfer function as it is.
The above approximation is merely established qualitatively at a low level. In reality, even when an amorphous thin film is employed, the image thereof has a specific distribution of spatial frequencies that is not uniform because of the radii of constituent atoms. Over an area where the spatial frequencies u exceed 0.1 nm−1, a scattering amplitude is known to rapidly fade because there is a limit to the scattering ability of constituent atoms to whatever of many atomic species the atoms belong. In other words, even when the diffractgram shown in FIG. 2A or the Young fringes shown in FIG. 2B are used to measure a contrast damping rate, the damping rate is not determined with an information transfer limit but with a variance in the quality of the amorphous thin film over a domain of frequencies equal to or larger than 0.1 nm−1 that should be noted in the future. There is therefore a high possibility that the information transfer limit dependent on an objective lens may be incorrectly assessed.
Further, the quality of the amorphous thin film 5 adopted as a specimen to be observed counts a lot inferably from the above description. For appropriate measurement, a homogeneous film having a film thickness of several tens of nanometers or less is needed. Moreover, an internal environment of an electron microscope such as contamination of a specimen largely affects measurement. For the appropriate measurement, preparation of a specimen and maintenance of an observational environment have to be achieved carefully.
As described in relation to the related art, an information transfer limit is expected to increase the significance as an index of performance of a transmission electron microscope that determines a resolution. In the past, a diffractram expressing an amorphous thin film is produced in order to estimate a phase contrast transfer function. However, as mentioned above, the result of measurement performed according to the conventional method largely depends on the quality of the amorphous thin film to be observed. Over a domain of resolutions that are equal to or smaller than 0.1 nm and that have come to be attainable in practice because an aberration correction technology has been put to practical use, the possibility that correct assessment cannot be achieved because there is a limit to homogeneity in the quality of the amorphous thin film gets higher.